Hello all, trivial question (of which however I'm not so sure): I have stock A that I expect to reach a certain value in X days, and I also have the beta coefficient of the relation of stock A and stock B over a comparable timeframe. (and yes they are highly correlated and cointegrated) (just to be sure we are talking about the same formula for beta, I'm referring to this one: returnY = alpha+beta*returnX) So.. how do I use the information above to infer stock B price in X days?
beta coefficient presumes normally distributed daily variance; in this case between 2 stocks - does such a thing actually exist and if so it must be large?
That's an odd definition of beta. Where did it come from? And what is 'alpha' in this case? The "normal" definition of beta is the volatility of a given asset against that of the market, not some perfectly locked "ratio of movement". There's no such thing, or we'd all be billionaires (if it did exist, you'd be able to construct a perfect hedge.) I'm feeling too lazy to hit the books at the moment, but Investopedia has an article that looks right: beta = covariance(SDev(name_returns))/variance(SDev(market_returns)) https://www.investopedia.com/ask/answers/070615/what-formula-calculating-beta.asp You may have been thinking about correlation... but that still doesn't provide, or even hint at, these stocks being somehow "locked together" so that one predicts the other. You don't. No such relationship exists.
Hi BWS, I looked it up a bit, actually there is not a single way to estimate beta because it's.. well, an estimation. Your method is fine and generally accepted, the method I use is to do a linear regression to find the best fit for the formula Y=alpha(the intercept)+beta(the slope coefficient)*X+e (residual), where obviously X and Y are the log returns of asset A and B. That's also taken from academic papers so I assume is correct (maybe it's a wrong assumption, but I'd rather trust someone whose math skill is infinitely better than mine) Regarding the perfect hedge, haha well that's something I'm working on.. For sure I can't predict the stock, but at least determining some upper/lower boundary I think should be feasible.. waddayuthink?
I prefer to think of it as a range rather than an estimation... the latter smacks a bit too much of the "finger in the wind" method of "science". Bell curves just, well, they make sense to me. Guessing (i.e., "estimation") doesn't. Oh, OK - now I get what you mean. I'm teaching data analysis this week, and I was just bitching my head off to my students about term and acronym abuse (e.g., the word "partition" is used in about a dozen different senses in the Big Data tech stack and the relevant analytics. FFS, people...) About half the greek alphabet should go stand in the corner and not be allowed to leave until it apologizes for all the confusion it's caused... Yeah, well, Black and Scholes would have loved for that assumption to hold true. Or even approximately true. I really, really, really doubt it. Price moves are best approximated as GBM - and there's no mean reversion, or any non-randomness to them (because if there was, the 'tutes would have arbed the living hell out of it - which would leave random noise.) It's very much like encryption and/or compression in CompSci: if you find repeated patterns, then your method is not a good one.
ok let's take one step back. Here I'm not trying to guess prices, but modeling a scenario, a "what if.. "case. So I assume that stock A in the future will get to price X. I have verified that stock A and B are not only correlated with a factor of beta but also cointegrated, which makes me optimistic about the possibility that the correlation will hold also in the future. At this point is it so crazy trying to find a reasonable band where stock B is likely to be sitting by that time?
A band? Sure - assuming no binary events occur on one side, the correlation continues to hold, and so on. The meaningful question is, will that band be narrow enough so you can extract alpha ( ) from it? My default take would be "no", for the same reason as the scenario above. If it's that trivial, it has long ago been spotted and arbed away. That's actually an extension of my thinking about TA and indicators: I'm willing to believe that they worked, to one degree or another, at some point. Then, computers came along - and squeezing the juice out of any easily-predictable movements became trivial (and therefore guaranteed.) P.S. Please note that I'm NOT trying to discourage you from testing it out; by all means, give it a shot - that's what paper trading is for. But it seems to me that the basic principle behind what I'm saying is strong enough to take it as a done deal. I'd love to be wrong, and for you to make a mint out of it.
It's the standard regression equation. Absolutely standard. The use of the letter "beta" for the vector (in this case a scalar) of regression coefficients precedes the use the term beta for stocks by, AFAIK, a century. Stock beta is a regression beta, that is where the term comes from. Alpha is the intercept. It works out exactly the same: "The univariate regression coefficient, beta, is defined as the covariance of x and y divided by the variance of the independent variable, x."
haha ok let's talk again in the future, when I'll be surely full of mint.. ..Or maybe full of something else
Not true for the equation as posted, not even true if the OP fitted that equation by OLS. You don't even need normality of the error term (residuals), however that does help with estimates of standard errors, confidence/prediction intervals, etc. Yes, commonly. For highly correlated assets, joint distribution of daily returns is usually elliptical (close to bivariate lnormal). For such assets, OLS regression is appropriate. OP mentions that the assets are also cointegrated. In that case OLS regression is superconsistent.